134 POPULAR SCIENCE MONTHLY. 



eluding remark that 'the reader is at liberty to draw any conclusion 

 he pleases from this diagram' only strengthens the impression that 

 the conclusion intended is considered unavoidable, though we are told 

 at the outset that ' the investigation is not to be looked upon as a final 

 solution of the principal problem.' 



Considering that it is now over fifteen years since the theory 

 of characteristic curves was first outlined and that no denial of it 

 has appeared, it must be taken for granted that the theory has found 

 general acceptance. It is for this reason that I undertook an investi- 

 gation, which proved laborious and unattractive in the main, in order 

 to combat with facts an error which to me seemed obvious from the 

 outset. The data which I have now at hand, though necessarily 

 meager, are amply sufficient to establish a duality, if not a multiplicity, 

 of characteristic curves for many authors. But this amounts to a 

 denial of Dr. Mendenhall's major premise, and consequently in- 

 validates his conclusion. Fig. 20, instead of furnishing a convincing 

 proof, or even contributary evidence, leaves the problem of disputed 

 authorship wholly untouched. In fact, my results throw considerable 

 doubt upon the very existence of characteristic curves in the sense 

 that the word has been employed by Dr. Mendenhall. I shall, there- 

 fore, use the term word-curve when referring to curves representing 

 the relative frequencies of different length words used in composition. 



Dr. Mendenhall states that the validity of his method as a test 

 of authorship implies two assumptions: first, that the author makes 

 use of a vocabulary which is peculiar to himself, and the character of 

 which does not change from year to year during his productive period ; 

 and second, that in the use of that vocabulary in composition, personal 

 peculiarities in the construction of sentences will, in the long run, 

 recur with such regularity that short words, long words and words of 

 medium length will occur with definite relative frequencies. 



These two assumptions are of course independent. Suppose it be 

 granted that authors use vocabularies peculiarly their own. It does 

 not at all follow that these peculiarities will manifest themselves in 

 varying word-lengths. Obviously an indefinite number of different 

 vocabularies is conceivable, each yielding the same average word-length 

 or even fitting to the same word-curve. Now, it is true that if authors 

 are endowed with a word-sense or word-instinct by means of which 

 personal traits are reflected through their vocabularies (first assump- 

 tion), and if, moreover, this word-sense manifests itself in measurable 

 differences in the relative frequencies of words of a given length 

 (second assumption), then these personal traits or peculiarities of an 

 author will in general modify the contour of the word-curve. But the 

 converse of this by no means follows, that the differences in the con- 



